Theorems · Theorem · order theory
neg_nonneg_of_nonpos
∀ {α : Type u} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α] {a : α}, a ≤ 0 → 0 ≤ -a- Defined in
- Mathlib.Algebra.Order.Group.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- neg_nonnegproof · cited by 60
Cited by9
Results whose statement or proof uses this declaration.
- MeasureTheory.integrableOn_Ioi_deriv_of_nonposproof · cited by 2
- smul_le_smul_of_nonpos_leftproof · cited by 1
- div_le_one_of_geproof · cited by 1
- MeasureTheory.integrable_add_iff_of_nonposproof · cited by 0
- IsRealClosed.of_linearOrderedFieldproof · cited by 0
- lt_of_smul_lt_smul_of_nonposproof · cited by 0
- Int.natAbs_inj_of_nonneg_of_nonposproof · cited by 0
- Int.natAbs_inj_of_nonpos_of_nonnegproof · cited by 0
- Int.natAbs_inj_of_nonpos_of_nonposproof · cited by 0